Exercise gives the acceleration a = d^2s/dt^2, initial velocity, and initial position of an object moving on a coordinate line. Find the object’s position at time t. a = -4 sin 2t, v(0) = 2, s(0) = -3

Simplify the expression. 3/5 ∛5 - 1/5 ∛5

a. The formula to convert from K to $^{\circ} \mathrm{C}$ is $t_{\mathrm{C}}=t_{\mathrm{K}}-273.15$. Find the formula used to convert from $^{\circ} \mathrm{C}$ to K. b. The formula to convert from $^{\circ} \mathrm{C}$ to $^{\circ} \mathrm{F}$ is $t_{v}=\frac{9}{5} \times t_{\mathrm{c}}+32$. Find the formula used to convert from $^{\circ} \mathrm{F}$ to $^{\circ} \mathrm{C}$.

On our moon, the acceleration of gravity is 1.6 m/sec^2. If a rock is dropped into a crevasse, how fast will it be going just before it hits bottom 30 sec later?

Exercise gives the velocity v = ds/dt and initial position of an object moving along a coordinate line. Find the object’s position at time t. v = 32t - 2, s(0.5) = 4

(a) Sketch lines through (0, 0) with slopes

$$1,0 , \frac { 1 } { 2 } , 2$$

, and -1. (b) Sketch lines through (0, 0) with slopes

$$\frac { 1 } { 3 } , \frac { 1 } { 2 } , - \frac { 1 } { 3 }$$

, and 3.

Suppose that a drop of mist is a perfect sphere and that, through condensation, the drop picks up moisture at a rate proportional to its surface area. Show that under these circumstances the drop’s radius increases at a constant rate.

Which of Aksum’s achievements has continued into modern times?

Express each decimal number in octal. 17. 34 18. 61 19. 223 20. 400 21. 1024 22. 12,340

It took 14 sec for a mercury thermometer to rise from -19 C to 100 C when it was taken from a freezer and placed in boiling water. Show that somewhere along the way the mercury was rising at the rate of 8.5 C/sec.

Consider the cubic function f(x) = ax^3 + bx^2 + cx + d. a. Show that f can have 0, 1, or 2 critical points. Give examples and graphs to support your argument. b. How many local extreme values can f have?

Choose the letter that best answers the question or complete s the statement. An alloy contains a. at least one metallic element. b. at least one nonmetallic element. c. only metallic elements. d. only nonmetallic elements.

Why are some of the benefits of a sole proprietorship also its greatest disadvantages?

Suppose that f(-1) = 3 and that f'(x) = 0 for all x. Must f(x) = 3 for all x? Give reasons for your answer.